Dynamic Constrained Economic/Emission Dispatch Scheduling Using Neural Network

Transcription

1 Dynamc Constraned Economc/Emsson Dspatch Schedulng Usng Neural Network Fard BENHAMIDA 1, Rachd BELHACHEM 1 1 Department of Electrcal Engneerng, IRECOM Laboratory, Unversty of Djllal Labes, , Sd Bel Abbes, Algera fard.benhamda@yahoo.fr, belhachem.rachd@yahoo.fr Abstract. In ths paper, a Dynamc Economc/Emsson Dspatch DEED) problem s obtaned by consderng both the economy and emsson objectves wth requred constrants dynamcally. Ths paper presents an optmzaton algorthm for solvng constraned combned economc emsson dspatch EED) problem and DEED, through the applcaton of neural network, whch s a flexble Hopfeld neural network FHNN). The constraned DEED must not only satsfy the system load demand and the spnnng reserve capacty, but some practcal operaton constrants of generators, such as ramp rate lmts and prohbted operatng zone, are also consdered n practcal generator operaton. The feasblty of the proposed FHNN usng to solve DEED s demonstrated usng three power systems, and t s compared wth the other methods n terms of soluton qualty and computaton effcency. The smulaton results showed that the proposed FHNN method was ndeed capable of obtanng hgher qualty solutons effcently n constraned DEED and EED problems wth a much shorter computaton tme compared to other methods. Keywords Dchotomy method, dynamc economc dspatch, envronmental dspatch, gas emsson, Hopfeld neural network, prohbted operatng zone. 1. Introducton Dynamc economc dspatch DED) s used to determne the optmal schedule of generatng outputs onlne so as to meet the load demand at the mnmum operatng cost under varous system and operatng constrants over the entre dspatch perods. DED s an extenson of the conventonal economc dspatch ED) problem that takes nto consderaton the lmts on the ramp rate of generatng unts to mantan the lfe of generaton equpment. Ths s one of the mportant optmzaton problems n a power system. Many approaches [1], [2], [3], [4], [5], [6] have been lsted to formulate and solve the ED problem; other methods [7], [8], [9], [10], [11], [12], [13], [14], [15], [16], [17], [18], [19], [20], are dedcated to solve DED. Currently, a large part of energy producton s done wth thermal sources. Thermal electrcal power generatng s one of the most mportant sources of carbon doxde CO 2 ), sulfur doxde SO 2 ) and ntrogen oxdes NO 2 ) whch create atmospherc polluton [7]. Emsson control has receved ncreasng attenton owng to ncreased concern over envronmental polluton caused by fossl based generatng unts and the enforcement of envronmental regulatons n recent years [18]. Numerous studes have emphaszed the mportance of controllng polluton n electrcal power systems [18], [19] and [20]. To get the choce n term of the best soluton between ED, EED, a good power management strategy s requred. Several optmzaton technques such as lambda teraton, lnear programmng L), nonlnear programmng NL), quadratc programmng Q) and nteror pont method IM) are employed for solvng the securty constraned economc dspatch and unt commtment problem [9]. Among these methods, the lambda teraton method has been appled n many software packages due to ts ease of mplementaton and used by power utltes for ELD [10]. Most of the tme, alone λ-method does not fnd the optmal soluton because of power system constrants. Therefore, the lambda method s used n conjuncton wth other optmzaton technques. The soluton of ED and DED problem usng genetc algorthm requred a large number of teratons/generatons when the power system has a large number of unts [5]. EED has been proposed n the feld of power generaton dspatch, whch smultaneously mnmzes both fuel cost and pollutant c 2013 ADVANCES IN ELECTRICAL AND ELECTRONIC ENGINEERING 1

2 emssons. When the emsson s mnmzed the fuel cost may be unacceptably hgh or when the fuel cost s mnmzed the emsson may be hgh. In lterature, EED s commonly known as envronmental ED or economc emsson dspatch, many algorthms are used to solve EED problem. Lterature [20] proposed a coolng mutaton technque n E algorthm to solve EED problem for 9-unt system. roposed methods n [12] convert a mult-objectve problem nto a sngle objectve problem by assgnng dfferent weghts to each objectve. Ths allows a smpler mnmzaton process but does requre the knowledge of the relatve mportance of each objectve and the explct relatonshp between the objectves usually does not exst. 2. DED roblem Formulaton The DED plannng must perform the optmal generaton dspatch for each perod t among the operatng unts to satsfy the system load demand, spnnng reserve capacty, and practcal operaton constrants of generators that nclude the ramp rate lmt and the prohbted operatng zone [16] ractcal Operaton Constrants 1) Ramp Rate Lmt Accordng to [2], [5] and [14], the nequalty constrants due to ramp rate lmts s gven as follows: t 1 t t 1 R up, 1) t R down, = 1,... Nand t = 1,... T, 2) where t s the output power at nterval t, and t 1 s the prevous output power. R up s the upramp lmt of the -th generator at perod t, MW/tme-perod); and R down s the downramp lmt of the -th generator MW/tme perod). 2) rohbted Operatng Zone References [1], [11], and [17] have shown the nputoutput curve for a typcal thermal unt wth valve ponts. These valve ponts generate many prohbted zones. In practcal operaton, adjustng the generaton output of a unt must avod unt operaton n the prohbted zones. Fgure 1 shows the nput output performance curve for a typcal thermal unt wth rohbted Zone. The feasble operatng zones of the unt can be descrbed as follows. Fg. 1: The nput output performance curve for a typcal thermal unt wth rohbted zone. t mn t l,1 u,j 1 t l,j u,n t max, j = 2, 3,... n, 3) where n s the number of prohbted zones of the -th generator.,1 l,,j u are the lower and upper power output of the prohbted zones j of the -th generator, respectvely ractcal Operaton Constrants The objectve of ED s to smultaneously mnmze the generaton cost rate and to meet the load demand of a power system over some approprate perod whle satsfyng varous constrants. To combne the above two constrants nto a ED problem, the constraned optmzaton problem at specfc operatng nterval can be modfed: T ) F T = t = = t=1 =1 T t=1 =1 F t a + b t ) + c t 2, 4) where F T j s the total generaton cost; F t t ) s the generaton cost functon of -th generator at perod t, whch s usually expressed as a quadratc polynomal or can be expressed n more complex form [3]; a, b, and c are the cost coeffcents of the -th generator; t s the power output of the -th generator and N s the number of generators commtted to the operatng system, T s the total perods of operaton. Subject to the followng constrants. 1) ower balance t = D t + L t, 5) =1 c 2013 ADVANCES IN ELECTRICAL AND ELECTRONIC ENGINEERING 2

3 where D t s the load demand at perod t and L t s the total transmsson losses of the same perod. Transmsson losses can be modeled ether by runnng a complete load flow analyss to the system [3] or by usng the loss coeffcents method also known as the B-coeffcents) developed by Kron and Krchmayer [13]. In the B-coeffcents method, the transmsson losses are expressed as a quadratc functon of the generaton level of each generator as follows: t = D t + L t, 6) =1 where D t s the load demand at perod t and L t s the total transmsson losses of the same perod. Transmsson losses can be modeled ether by runnng a complete load flow analyss to the system [3] or by usng the loss coeffcents method also known as the B-coeffcents) developed by Kron and Krchmayer [13]. In the B-coeffcents method, the transmsson losses are expressed as a quadratc functon of the generaton level of each generator as follows: L t = t B j j t + B 0 t + B 00, 7) =1 j=1 =1 where B, B 0 and B 00 are the loss-coeffcent matrx, the loss-coeffcent vector and the loss constant, respectvely, or approxmately [3], [18]: L t = =1 j=1 t B j j t. 8) 2) System spnnng reserve constrants N max =1 mn t, Rup )) SR t, t = 1, 2,..., T. 9) 3) Generator operaton constrants max mn, t 1 mn max, t 1 ) R down R up ), 10) where mn and max are the mnmum and maxmum outputs of the -th generator respectvely. The output t must fall n the feasble operatng zones of unt by satsfyng the constrant descrbed by Eq. 3) Dynamc Economc and Emsson Dspatch In an ED problem, the gas emsson s not consdered. The gas emsson from a conventonal thermal generator unt depends on the power generaton. Lke the fuel cost, total gas emsson can be approxmated by a quadratc functon of Eg. 11), [19]. The emsson dspatch problem can be descrbed as the optmzaton of total gas emsson defned by: E T = α 2 ) + β + γ, 11) =1 where E T s the total amount of emsson ton/h) whch can be SO 2 or NO x or any other gas; α, β and γ, are the coeffcent of generator emsson characterstcs. The gas emsson dspatch can be done n parallel wth a ED problem by ncludng emsson cost. Dfferent types of emssons are modeled n lterature as a cost n addton to the fuel cost. In fact, DEED s a mult-objectve problem. But DEED can be transformed nto sngle objectve optmzaton problem by usng a prce penalty factor [7]: mn φ T = F T ) + he T ) = T = F T ) T + h E T ) T = = t=1 =1 T t=1 =1 a + b T ) + c T 2 + +h α + β T + γ T ) 2 ) = = T t=1 =1 á + b T ) + ć T 2, 12) where φ T s the total cost of the system; á, b and ć are the combned cost and emsson functon coeffcents and h s the prce penalty factor n $/kg) for unt wth: á = a + h α, 13) b = b + h β, 14) ć = c + h γ, 15) h = F T max ) E T max ). 16) Equaton 12) s subjected to the prevous constrants of Eq. 5) to Eq. 9). A tunng for problem formulaton s ntroduced through two weght factors k 1 and k 2 as follow: mn φ T = k 1 F T ) + k 2 he T ). 17) For k 1 = 1 and k 2 = 0 the soluton wll gve results of ED. For k k 1 = 0 and k 2 = 1 results wll gve emsson dspatch and for k 1 = k 2 = 1, DEED results can be obtaned. c 2013 ADVANCES IN ELECTRICAL AND ELECTRONIC ENGINEERING 3

4 3. A Flexble FHNN Appled to Combned Economc and Emsson Dspatch The HNN model wth contnuous output varables and a contnuous and monotoncally ncreasng transfer functon f U ) have a dynamc characterstc of each neuron whch can be descrbed by: du d t = I + T j V j. 18) j=1 where U s the total nput of neuron ; V s the output of neuron ; T j s the nterconnecton conductance from the output of neuron j to the nput of neuron ; T s the self-connecton conductance of neuron and I s the external nput to neuron and t s a dmensonless varable. The model s a mutual couplng neural network and wth of non-herarchcal structure. It has been proved [13] that the contnuous Hopfeld model state through the computaton process always moves n such a way that energy converges to a mnmum, whch can be defned as [18]: E = 1 2 T j V V j I V. 19) =1 j=1 = Mappng of EED nto the Hopfeld model To map the EED problem usng the Hopfeld method, the energy functon E ncludng both power msmatch, m and total fuel cost F fuel and emsson) can be stated as follows [13], [15], [17], [19]: E = A N 2 =1 á + b t + ć t)2 + D t + L t ) ) N t, 20) + B 2 where t = 1,..., T ; t s the power output of the - th generator for t tme perod; A and B are postve weghtng factors. The nputoutput model of HNN s the sgmod functon: V max V = V mn + ) V mn 1 + tanh U )) u 0, 21) wth a shape constant u 0 of the sgmodal functon. Comparng the energy functon Eq. 20) wth the Hopfeld energy functon Eq. 19), we get the nterconnecton conductances, the self-connecton and the external nputs, respectvely: T j = A Bć, 22) T = A, 23) I = AD + L) B b ). 24) 2 The HNN solves the statc part of the EED problem wthout consderng transmsson losses. To enforce ths constrant nto the soluton, a dchotomy soluton method as descrbed n [13] s done to obtan a EED soluton ncludng losses. The proposed algorthm s ntroduced as follows. For each tme perod t, do the followng: step 1: Intalzaton of the nterval search [D 3 D 1 ], where D 3 s the power demand at perod t and D 1 s a maxmum forecast of demand plus losses at the same perod t. ɛ a pre-specfed tolerance. Intalze the teraton counter k = 1. D k 3 = D; D k 2 = D k 1, step 2: Determne the optmal generators power outputs usng the HNN algorthm of [13], by neglectng losses and settng the power demand as D k D k 2, step 3: Calculate the transmsson losses L k for the current teraton k usng Eq. 6), step 4: If D k 1 D k 3 < ɛ, stop otherwse go to step 5, step 5: If D2 k L k < D, update D 3 and D 2 for the next teraton ) as follows. D1 k+1 = D2; k D2 k D k 2 D3 k. Replace k by k + 1 and go to step A Strategy for the rohbted Zone roblem To prevent the unts from fallng n prohbted zones durng the dspatchng process, we use a strategy to take care of t. In the strategy, we ntroduce a medum producton pont,,j M,j, for the j-th prohbted zone of unt. The correspondng ncremental cost, λ M,j, s defned by: [ ) )] F u,j F l,j λ M,j = u,j l,j). 25) For each perod t, a mnmum and maxmum outputs of the -th generator s modfed as follow: mn,t = max mn, t 1 R down ), 26) max,t = mn max, t 1 R up ). 27) For the fuel cost functons, the ncremental cost λ M,j s equal to the average cost of the prohbted zone. The medum pont dvdes t nto 2 subzones: c 2013 ADVANCES IN ELECTRICAL AND ELECTRONIC ENGINEERING 4

5 Tab. 1: The 3-Unt system data. max mn a b c R up R down Unt MW) MW) $/h) $/MWh) $/MW 2 h) $/MWh) $/MWh) ,29 0, ,85 0, ,97 0, case 1: The prohbted zone s wthn the mnmum and maxmum generator s outputs of the perod t. Dspatch unt wth generaton level at or above,j u f the system s ncremental cost exceeds λ M mn,t,j, by settng =,j u. Conversely, dspatch unt wth generaton level at or below,j l, f the system ncremental cost s less than λ M max,t,j, by settng =,j l, case 2: The mnmum generator s output allowed of the perod t exceeds the lower bound of the prohbted zone. Dspatch unt by settng mn,t =,j u, case 3: The maxmum generator s output allowed of the perod t s less than the upper bound of the prohbted zone. Dspatch unt by settng max,t =,j l. When a unt operates n one of ts prohbted zones, the dea of ths strategy s to force the unt ether to escape from the left subzone and go toward the lower bound of that zone or to escape from the rght subzone and go toward the upper bound of that zone. 5. Computatonal rocedures of FHNN for DEED Based on the employment of the strategy mentoned above, the computatonal steps for the proposed approach for solvng the DEED wth a gven number of dspatch ntervals T e.g. one day) are summarzed as follows: step 0: Let k 1 = k 2 = 1 n Eq. 17). Specfy the generaton for all unts, at t 1 dspatch nterval. Calculate the combned cost and emsson functon coeffcents á, b and ć usng Eq. 13) to Eq. 16), step 1: At t dspatch nterval, specfy the lower and upper bound generaton power of each unt usng Eq. 26) and Eq. 27), a manner to satsfy the ramp rate lmt. ck the hourly power demand D t. Apply the algorthm based on HNN model of [13] to determne the optmal generaton for all unts wthout consderng transmsson losses and the prohbted zones, step 2: Apply the hybrd algorthm of Secton 3, based on dchotomy method to adjust the optmal generaton of step 1 for all unts, to nclude transmsson losses, step 3: If no unt falls n the prohbted zone, the optmal generaton obtaned n Step 2 s the soluton, go to Step 5; otherwse, go to Step 4, step 4: Apply the strategy of Secton 4 to escape from the prohbted zones, and redspatch the unts havng generaton fallng n the prohbted zone, step 5: Let t = t + 1 and f t T, then go to Step 1. Otherwse, termnate the computaton. The FHNN can be modfed to handle EED as follow: set the number of dspatch nterval to 1 t = 1), let R up = R down =, snce the ramp rate lmts were not taken nto account n EED and classcal ED, escape step 4 n the procedure f prohbted zones of unts s not taken nto account. The proposed FHNN can be modfed to handle smply DED by settng k 1 = 1, k 2 = 0 n Eq. 17) or can be modfed to handle emsson ED by settng k 1 = 0, k 2 = 1 n Eq. 17). 6. Numercal Examples and Results In order to valdate the proposed procedure and to verfy the feasblty of the FHNN method to solve the DEED, a 3-unt system s tested. The proposed method s mplemented wth the graphcal language LabVIEW on a entum 4, 3 GHz. The data s gven n Tab. 1 and the prohbted zones are gven n Tab. 2, [19]. The load demand vares from 550 to 900 MW as shown n Tab. 3. The emsson functons coeffcents are gven n Tab. 4 and Tab. 5 for SO 2 ) and NO x ) emsson respectvely. Transmsson losses are calculated usng Eq. 8). The transmsson B-coeffcents are gven by: B = [0, , , 00012], B j = 0. 28) c 2013 ADVANCES IN ELECTRICAL AND ELECTRONIC ENGINEERING 5

6 Here, for comparson, we have appled the proposed method to the DED see Tab. 6), the SO 2 ) emsson dynamc dspatch see Tab. 7), the NO x ) emsson dynamc dspatch see Tab. 8), the combned SO 2 ) emsson and economc dspatch see Tab. 9) and the combned NO x ) emsson and economc dspatch see Tab. 10). Tab. 2: rohbted zones of generatng unts of 3-Unt system. Unt rohbted zone MW) 1 [ ] [ ] 2 [ ] [ ] The results of the FHNN method for the combned dynamc emsson/economc dspatch are shown n Tab. 9 and Tab. 10 for SO 2 and NO x emsson, respectvely. The producton cost s lower than the emsson dspatches and the latter are hgher than the emsson dspatches. The executon tme of the FHNN for the 3-unt system s about 0,01 seconds for all cases. Through the comparson of smulatons results of Tab. 11, t can be seen that the proposed method has the best soluton qualty and calculaton tme compared to the other methods. Tab. 3: The daly load demand MW) of 3-Unt system. Hour Load Tab. 4: SO 2 emsson data of 3-Unt system. α SO2 β SO2 γ SO2 ton/h) ton/mwh) ton/mw 2 h) 0, , e 6 0, , ,4658 e 6 0, , ,4658 e 6 Tab. 5: NO 2 emsson data of 3-Unt system. α NOx β NOx γ NOx ton/h) ton/mwh) ton/mw 2 h) 0, , e 6 1, e 7 0, , e 5 3, e 7 0, , e 4 1, e 6 The results from [18] and reported n Tab. 11 showed that the proposed HNN method was ndeed capable of obtanng hgher qualty soluton effcently n constraned DED problems, compared wth those obtaned by the FE, IFE, and SO algorthms from [10], [15] n terms generaton cost and average computatonal tme. The same method s used to solve classcal DED. The Tab. 6 summarzes the results of classcal DED soluton usng FHNN method for the sx tme nterval, ncludng power generaton for the three unts, producton costs, lne losses, the NO x and SO 2 emssons n ton/h). It can be seen from the results that the prohbted zone and the ramp rate lmt constrants are respected. The results of the FHNN for NO x and SO 2 mnmum emsson dspatch of the same test system are shown n Tab. 7 and Tab. 8 respectvely. From the tables, for each tme nterval, the producton cost s greater than the producton cost n the case of classcal DED see Tab.6), because the objectves are dfferent, n Tab. 7 and Tab. 8, the objectve s to obtan the mnmum gas emsson NO x and SO 2, respectvely. Contrarly n Tab. 7 and Tab. 8, gas emsson NO x and SO2 are lower than those resulted from classcal DED soluton mnmum cost), respectvely. 7. Concluson The DEED plannng must perform the optmal generaton dspatch at the mnmum operatng cost and emsson among the operatng unts to satsfy the system and practcal operaton constrants, of generators. In ths paper, we have successfully employed a flexble HNN method to solve both the DEED and EED problems wth generator constrants. In relaton to the procedure nvolved n solvng the DEED and DED, the smulaton results acheved by FHNN to the case studes of 3-unts, 6 and 15-unt, respectvely, demonstrated that the proposed method has superor features, ncludng hgh-qualty soluton and good computaton effcency. The results of these smulatons wth FHNN approaches are very encouragng and represent an mportant contrbuton to neural network setups. Methods combnng HNN wth evolutonary methods can be very effectve n solvng DEED and EED problems. In the future, we wll focus manly on the concepton of such hybrd approaches. References [1] LEE, F. N. and A. M. BREIOHL. Reserve Constraned Economc Dspatch wth rohbted Operatng Zones. IEEE Transactons on ower Systems. 1993, vol. 8, ss. 1, pp ISSN DOI: / [2] WALTERS, D. C. and G. B. SHEBLE. Genetc Algorthm Soluton of Economc Dspatch wth Valve ont Loadng. IEEE Transactons on ower Systems. 1993, vol. 8, ss. 3, pp ISSN DOI: / [3] YANG, H. T.,. C. YANG and C. L. HUANG. Evolutonary rogrammng Based Economc Dspatch for Unts wth Non-Smooth Fuel Cost Functons. IEEE Transactons on ower Systems. 1996, vol. 11, ss. 1, pp ISSN DOI: / c 2013 ADVANCES IN ELECTRICAL AND ELECTRONIC ENGINEERING 6

7 Tab. 6: Classcal DED mnmum cost) usng FHNN method. Interval/Unt ,65 279,77 328,18 401,23 425,70 475, ,88 243,30 282,27 341,09 360,79 400, ,66 85,47 101,16 124,83 132,76 148,760 L MW) 7,19 8,55 11,62 17,17 19,26 23,82 D MW) F T $) 5578, , , , , ,72 SO 2 ton/h) 6, , , , ,009 11,1651 NO X ton/h) 0, , , , , ,11504 Tab. 7: Emsson NO X dspatch mnmum NO X ) usng FHNN method. Interval/Unt ,30 343,03 408,70 507,76 540,93 600, ,17 171,12 203,13 251,40 267,57 306, ,550 93,044 98, , , ,200 L MW) 6,03 7,20 9,87 14,76 16,62 20,82 D MW) F T $) 5583, , , , , ,76 SO 2 ton/h) 6, , , , , ,8467 NO X ton/h) 0, , , , , ,10676 Tab. 8: Emsson SO 2 dspatch mnmum SO 2 ) usng FHNN method. Interval/Unt ,14 453,64 532,98 600,00 600,00 600, ,00 100,00 100,00 137,98 163,76 219, ,77 77,15 126,44 152, L MW) 6,140 7,410 10,130 14,431 15,993 19,950 D MW) F T $) 5638, , , , , ,61 SO 2 ton/h) 6, , , , , ,74760 NO X ton/h) 0, , , , , ,12319 Tab. 9: The combned SO 2 emsson/ economc dspatch usng FHNN method. Interval/Unt ,18 292,23 348,51 433,36 461,77 518, ,31 226,38 254,60 297,14 311,39 339, ,420 89, , , , ,920 L MW) 6,920 8,130 10,860 9,312 17,620 21,660 D MW) F T $) 5576, , , , , ,42 SO 2 ton/h) 6, , , , , ,9662 NO X ton/h) 0, , , , , ,11324 Tab. 10: The combned NO X emsson /economc dspatch usng FHNN method. Interval/Unt ,53 330,76 373,42 437,81 459,51 502, , , , , , , ,11 93,61 102,65 116,31 120,91 130,12 L MW) 6,05 7,34 10,38 15,93 18,36 23,32 D MW) F T $) 5582, , , , , ,11 SO 2 ton/h) 6, , , , , ,1108 NO X ton/h) 0, , , , , , Tab. 11: The summary of the daly generaton cost and CU tme. Method Total Cost $) CU tme 6-Unts 15-Unts 6-Unts 5-Unts FE [10] 315, , , ,630 IFE [10] 315, , ,06 574,85 SO [18] 314, ,131 2,27 3,31 FHNN, proposed 313, ,796 1,52 2,22 c 2013 ADVANCES IN ELECTRICAL AND ELECTRONIC ENGINEERING 7

8 [4] SINHA, N., R. CHAKRABARTI and. K. CHATTOADHYAY. Evolutonary rogrammng Technques for Economc Load Dspatch. IEEE Transactons on Evolutonary Computaton. 2003, vol. 7, ss. 1, pp ISSN X. DOI: /TEVC [5] CHEN,. H. and H. C. CHANG. Large- Scale Economc Dspatch by Genetc Algorthm. IEEE Transactons on ower Systems. 1995, vol. 10, ss. 4, pp ISSN DOI: / [6] BENHAMIDA, F., R. BELHACHEM, S. SOUAG and A. BENDAOUED. A Fast Solver for Combned Emsson and Generaton Allocaton Usng a Hopfeld Neural Network. In: Innovatons n Intellgent Systems and Applcatons IN- ISTA): 2012 Internatonal Symposum on. Trabzon: IEEE, 2012, pp ISBN DOI: /INISTA [7] VENKATESH,., R. GNANADASS and N.. ADHY. Comparson and Applcaton of Evolutonary rogrammng Technques to Combned Economc Emsson Dspatch wth Lne Flow Constrants. IEEE Transactons on Evolutonary Computaton. 2003, vol. 18, ss. 2, pp ISSN DOI: /T- WRS [8] ATTAVIRIYANUA,., H. KITA, E. TANAKA and J. HASEGAWA. A Hybrd E and SQ for Dynamc Economc Dspatch wth Nonsmooth Fuel Cost Functon. IEEE Transactons on ower Systems. 2002, vol. 17, ss. 2, pp ISSN DOI: /T- WRS [9] XIA, X. and A. M. ELAIW. Optmal Dynamc Economc Dspatch of Generaton: a Revew. Electrc ower Systems Research. 2010, vol. 80, ss. 8, pp ISSN DOI: /j.epsr [10] GAING, Z. L. Constraned Dynamc Economc Dspatch Soluton Usng artcle Swarm Optmzaton. In: IEEE ower Engneerng Socety General Meetng. Denver: IEEE, 2004, vol. 1, pp ISBN DOI: /ES [11] YUAN, X., A. SU, Y. YUAN, H. NIE a L. WANG. Non-convex dynamc dspatch of generators wth prohbted operatng zones. Optmal Control Applcatons and Methods. 2009, vol. 30, ss. 1, pp ISSN DOI: /oca.873. [12] HEMAMALINI, S. and S.. SIMON. Emsson Constraned Economc wth Valve ont Effect Usng artcle Swarm Optmzaton. TENCON 2008 IEEE Regon 10. Conference. Hyderabad: IEEE, 2008, pp ISBN DOI: /TENCON [13] BENHAMIDA, F., A. BENDAOUD and K. MEDLES. Generaton Allocaton roblem Usng a Hopfeld-Bsecton Approach Includng Transmsson Losses. Internatonal Journal of Electrcal ower & Energy Systems. 2011, vol. 33, ss. 5, pp ISBN DOI: /j.jepes [14] OTHIYA, S., I. NGAMROOB and W. KONG- RAWECHNOMAS. Applcaton of Multple Tabu Search Algorthm to Solve Dynamc Economc Dspatch Consderng Generator Constrants. Energy Converson and Management. 2008, vol. 49, ss. 4, pp ISBN DOI: /j.enconman [15] SU, C. T. and C. T. LIN. New Approach wth a Hopfeld Modelng Framework to Economc Dspatch. IEEE Transactons on ower Systems. 2000, vol. 15, ss. 2, pp ISSN DOI: / [16] COELHO, L. D. S. and C. S. LEE. Solvng Economc Load Dspatch roblems n ower Systems Usng Chaotc and Gaussan artcle Swarm Optmzaton Approaches. Internatonal Journal of Electrcal ower & Energy Systems. 2008, vol. 30, ss. 5, pp ISSN DOI: /j.jepes [17] SU, C. T. and G. J. CHIOU. An Enhanced Hopfeld Model for Economc Dspatch Consderng rohbted Zones. Electrc ower Systems Research. 1997, vol. 42, no. 1, pp ISSN [18] BENHAMIDA, F., A. BENDAOUD, K. MEDLES and A. TILMATINE. Dynamc Economc Dspatch Soluton wth ractcal Constrants Usng a Recurrent Neural Network. rzeglad Elektrotechnczny. 2011, vol. 87, ss. 8, pp ISSN [19] GUTA, D. Envronmental Economc Load Dspatch Usng Hopfeld Neural Network. Ms. Thess Thapar Unversty, atala. Avalable at: [20] BASU, M. Dynamc Economc Emsson Dspatch Usng Evolutonary rogrammng and Fuzzy Satsfed Method. Internatonal Journal of Emergng Electrc ower Systems. 2007, vol. 8, ss. 4, pp ISSN X. c 2013 ADVANCES IN ELECTRICAL AND ELECTRONIC ENGINEERING 8

9 About Authors Fard BENHAMIDA was born n n Ghazaouet Algera). He receved, the M.Sc. degree from Unversty of technology, Bagdad, Iraq, n 2003, and the h.d. degree from Alexandra Unversty, Alexandra, Egypt, n 2006, all n electrcal engneerng. resently, he s an Assstant rofessor n the Electrcal Engneerng Department and a Research Scentst n the IRECOM laboratory n unversty of Bel-Abbs. Hs research nterests nclude power system analyss, computer aded power system; unt commtment, economc dspatch. Rachd BELHACHEN was born n Tlemcen Algera). He receved M.Sc. degree from Djlal Labes unversty of Sd Bel-Abbs, Algera, n He prepares the h.d. degree n the same unversty, all n electrcal engneerng. Hs research nterests nclude power system analyss and renewable energy. c 2013 ADVANCES IN ELECTRICAL AND ELECTRONIC ENGINEERING 9